Valutazione della qualità ed autenticità di prodotti oleari e lattiero caseari mediante metodi fisici di analisi accoppiati a tecniche statistiche multivariate

Questa tesi descrive alcuni studi di messa a punto di metodi di analisi fisici accoppiati con tecniche statistiche multivariate per valutare la qualità e l’autenticità di oli vegetali e prodotti caseari. L’applicazione di strumenti fisici permette di abbattere i costi ed i tempi necessari per le analisi classiche ed allo stesso tempo può fornire un insieme diverso di informazioni che possono riguardare tanto la qualità come l’autenticità di prodotti. Per il buon funzionamento di tali metodi è necessaria la costruzione di modelli statistici robusti che utilizzino set di dati correttamente raccolti e rappresentativi del campo di applicazione. In questo lavoro di tesi sono stati analizzati oli vegetali e alcune tipologie di formaggi (in particolare pecorini per due lavori di ricerca e Parmigiano-Reggiano per un altro). Sono stati utilizzati diversi strumenti di analisi (metodi fisici), in particolare la spettroscopia, l’analisi termica differenziale, il naso elettronico, oltre a metodiche separative tradizionali. I dati ottenuti dalle analisi sono stati trattati mediante diverse tecniche statistiche, soprattutto: minimi quadrati parziali; regressione lineare multipla ed analisi discriminante lineare.

Development of methodologies for fish freshness assessment using metabonomics applications.

This study focuses on the use of metabonomics applications in measuring fish freshness in various biological species and in evaluating how they are stored. This metabonomic approach is innovative and is based upon molecular profiling through nuclear magnetic resonance (NMR). On one hand, the aim is to ascertain if a type of fish has maintained, within certain limits, its sensory and nutritional characteristics after being caught; and on the second, the research observes the alterations in the product’s composition. The spectroscopic data obtained through experimental nuclear magnetic resonance, 1H-NMR, of the molecular profiles of the fish extracts are compared with those obtained on the same samples through analytical and conventional methods now in practice. These second methods are used to obtain chemical indices of freshness through biochemical and microbial degradation of the proteic nitrogen compounds and not (trimethylamine, N-(CH3)3, nucleotides, amino acids, etc.). At a later time, a principal components analysis (PCA) and a linear discriminant analysis (PLS-DA) are performed through a metabonomic approach to condense the temporal evolution of freshness into a single parameter. In particular, the first principal component (PC1) under both storage conditions (4 °C and 0 °C) represents the component together with the molecular composition of the samples (through 1H-NMR spectrum) evolving during storage with a very high variance. The results of this study give scientific evidence supporting the objective elements evaluating the freshness of fish products showing those which can be labeled “fresh fish.”

Modelling and classification with quantile-based distributions

In this work, we explore and demonstrate the potential for modeling and classification using quantile-based distributions, which are random variables defined by their quantile function. In the first part we formalize a least squares estimation framework for the class of linear quantile functions, leading to unbiased and asymptotically normal estimators. Among the distributions with a linear quantile function, we focus on the flattened generalized logistic distribution (fgld), which offers a wide range of distributional shapes. A novel naïve-Bayes classifier is proposed that utilizes the fgld estimated via least squares, and through simulations and applications, we demonstrate its competitiveness against state-of-the-art alternatives. In the second part we consider the Bayesian estimation of quantile-based distributions. We introduce a factor model with independent latent variables, which are distributed according to the fgld. Similar to the independent factor analysis model, this approach accommodates flexible factor distributions while using fewer parameters. The model is presented within a Bayesian framework, an MCMC algorithm for its estimation is developed, and its effectiveness is illustrated with data coming from the European Social Survey. The third part focuses on depth functions, which extend the concept of quantiles to multivariate data by imposing a center-outward ordering in the multivariate space. We investigate the recently introduced integrated rank-weighted (IRW) depth function, which is based on the distribution of random spherical projections of the multivariate data. This depth function proves to be computationally efficient and to increase its flexibility we propose different methods to explicitly model the projected univariate distributions. Its usefulness is shown in classification tasks: the maximum depth classifier based on the IRW depth is proven to be asymptotically optimal under certain conditions, and classifiers based on the IRW depth are shown to perform well in simulated and real data experiments.

Longterm peripheral baroreflex and chemoreflex function after bilateral eversion carotid endarterectomy

Introduction The “eversion” technique for carotid endarterectomy (e-CEA), that involves the transection of the internal carotid artery at the carotid bulb and its eversion over the atherosclerotic plaque, has been associated with an increased risk of postoperative hypertension possibly due to a direct iatrogenic damage to the carotid sinus fibers. The aim of this study is to assess the long-term effect of the e-CEA on arterial baroreflex and peripheral chemoreflex function in humans. Methods A retrospective review was conducted on a prospectively compiled computerized database of 3128 CEAs performed on 2617 patients at our Center between January 2001 and March 2006. During this period, a total of 292 patients who had bilateral carotid stenosis ≥70% at the time of the first admission underwent staged bilateral CEAs. Of these, 93 patients had staged bilateral e-CEAs, 126 staged bilateral s- CEAs and 73 had different procedures on each carotid. CEAs were performed with either the eversion or the standard technique with routine Dacron patching in all cases. The study inclusion criteria were bilateral CEA with the same technique on both sides and an uneventful postoperative course after both procedures. We decided to enroll patients submitted to bilateral e-CEA to eliminate the background noise from contralateral carotid sinus fibers. Exclusion criteria were: age >70 years, diabetes mellitus, chronic pulmonary disease, symptomatic ischemic cardiac disease or medical therapy with b-blockers, cardiac arrhythmia, permanent neurologic deficits or an abnormal preoperative cerebral CT scan, carotid restenosis and previous neck or chest surgery or irradiation. Young and aged-matched healthy subjects were also recruited as controls. Patients were assessed by the 4 standard cardiovascular reflex tests, including Lying-to-standing, Orthostatic hypotension, Deep breathing, and Valsalva Maneuver. Indirect autonomic parameters were assessed with a non-invasive approach based on spectral analysis of EKG RR interval, systolic arterial pressure, and respiration variability, performed with an ad hoc software. From the analysis of these parameters the software provides the estimates of spontaneous baroreflex sensitivity (BRS). The ventilatory response to hypoxia was assessed in patients and controls by means of classic rebreathing tests. Results A total of 29 patients (16 males, age 62.4±8.0 years) were enrolled. Overall, 13 patients had undergone bilateral e-CEA (44.8%) and 16 bilateral s-CEA (55.2%) with a mean interval between the procedures of 62±56 days. No patient showed signs or symptoms of autonomic dysfunction, including labile hypertension, tachycardia, palpitations, headache, inappropriate diaphoresis, pallor or flushing. The results of standard cardiovascular autonomic tests showed no evidence of autonomic dysfunction in any of the enrolled patients. At spectral analysis, a residual baroreflex performance was shown in both patient groups, though reduced, as expected, compared to young controls. Notably, baroreflex function was better maintained in e-CEA, compared to standard CEA. (BRS at rest: young controls 19.93 ± 2.45 msec/mmHg; age-matched controls 7.75 ± 1.24; e-CEA 13.85 ± 5.14; s-CEA 4.93 ± 1.15; ANOVA P=0.001; BRS at stand: young controls 7.83 ± 0.66; age-matched controls 3.71 ± 0.35; e-CEA 7.04 ± 1.99; s-CEA 3.57 ± 1.20; ANOVA P=0.001). In all subjects ventilation (VÝ E) and oximetry data fitted a linear regression model with r values > 0.8. Oneway analysis of variance showed a significantly higher slope both for ΔVE/ΔSaO2 in controls compared with both patient groups which were not different from each other (-1.37 ± 0.33 compared with -0.33±0.08 and -0.29 ±0.13 l/min/%SaO2, p<0.05, Fig.). Similar results were observed for and ΔVE/ΔPetO2 (-0.20 ± 0.1 versus -0.01 ± 0.0 and -0.07 ± 0.02 l/min/mmHg, p<0.05). A regression model using treatment, age, baseline FiCO2 and minimum SaO2 achieved showed only treatment as a significant factor in explaining the variance in minute ventilation (R2= 25%). Conclusions Overall, we demonstrated that bilateral e-CEA does not imply a carotid sinus denervation. As a result of some expected degree of iatrogenic damage, such performance was lower than that of controls. Interestingly though, baroreflex performance appeared better maintained in e-CEA than in s-CEA. This may be related to the changes in the elastic properties of the carotid sinus vascular wall, as the patch is more rigid than the endarterectomized carotid wall that remains in the e-CEA. These data confirmed the safety of CEA irrespective of the surgical technique and have relevant clinical implication in the assessment of the frequent hemodynamic disturbances associated with carotid angioplasty stenting.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.